[tex] 47\frac {1}{2}\ gallons[/tex]
Step-by-step explanation:
Taking into consideration that no significant leakages occur from storage and the reserve is used only for agriculture then, the amount consumed will be equivalent to [tex]24\frac {3}{4}-\ 15\frac {1}{4}=9\frac {1}{2}[/tex]
For 5 days, the quantity reduces by 9.5*5=47.5 gallons
Therefore, the barrel would have changed by [tex] 47\frac {1}{2}\ gallons[/tex]